A gas is contained in a vertical, frictionless piston-cylinder device. The piston has a mass of mpiston = 2 kg and a cross-sectional area of Apiston = 30 cm2 . A spring above the piston is compressed by s = 2.5 mm and has a spring constant k = 38 kN m . a) If the atmospheric pressure is p[infinity] = 1 atm, determine the initial pressure p1 inside the cylinder. Heat is added to the system until the piston moves an additional 10 mm.

105146 Pa

1) We will make a Free-Body Diagram representing all the upward and downward pressures exerted on the piston.

2) We will formulate an equation balancing all upward and downward pressures.

     P1= Patm + Pw + Pspring

3) We will calculate each of the pressures separately.

          P = F/A

          F= ks

          k= 38×1000 =38000 N m

          s= 2.5 /1000 = (2.5x10^-3) m

          F = 38000×(2.5x10^-3) = 95 N

          A = 30/10000 = (30x10^-4) m2

          P = 95 / (30x10^-4)

          Pspring ≅ 3167 Pa

          P = F/A

          F = W = mg

          W = 2×9.81 = 19.62 N

          A = 30/10000 = (30x10^-4) m2

          P = 19.62 / (30x10^-4)

          Pw = 654 Pa

        P = 1atm = 101325 Pa

        Patm = 101325 Pa

4) We will add all the downward pressures to reach the final answer (initial pressure inside the cylinder).

       P1= Patm + Pw + Pspring

       P1= 101325+654+3167

       P1= 105146 Pa

he made 11 calls in one day

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day